Pricing life insurance products in Iran using fuzzy interest rates

One of the most important problems involved insurance companies is insurance products pricing. In recent actuarial researches, fuzzy random variables have been used to consider uncertainty of economics parameters in insurance products pricing. Due to the effects of interest rate uncertainty on the insurance industry and especially life insurance, in this article, fuzzy random variables are implemented to consider interest rate uncertainty and calculate premiums for different types of life insurance products. Also, considering that the life table of Iran has been written based on the demographic information of this country and has been communicated to insurance companies to use, the results of using this table on fuzzy insurance premiums of different types of insurance policies have been compared with the life table TD88-90 previously used by insurance companies.

In this study, the fuzzy interest rates are used to define fuzzy discount functions and premiums of life insurance products is calculated.

In this paper, we have implemented fuzzy set theory to model interest rate for calculating premiums of life insurance products. Research findings were presented and analyzed for (term and whole) life insurances, endowments and life annuities using the interest rates announced in the supplement of Regulation No. 68 for Iranian life Insurance products. The premium calculations have been performed for Life table of Iran, which recently has been issued to be used by insurance companies, and life table TD88-90, which has previously been used by insurance companies.  Our findings based on Life table of Iran for a life annuity shows that all possible values of the premium for a 57-year-old person are in the interval [3.741, 4.384] and the deterministic amount of premium is 4.045. Also, the net premiums for the average risk aversion mode (β =0.75) is 4.212. Also, the effect of changes in β and insured age on premium amounts for different types of life insurance products has been studied and analyzed.  Furthermore, all calculations based on life table TD88-90 has been done and is compared with those based on Life table of Iran. Theoretically, the mortality probability of an x-year-old person according to the Life table of Iran is higher than the mortality probability of this person based on the life table TD88-90. So, the premiums calculated for this person based on the Iranian table for term insurance and endowment insurance are less and for life annuity is more than the premium calculated based on Table TD88-90. This can also be seen based on the findings of this article. On the other words, our findings based on table TD88-90 shows that all possible values of the fuzzy premium for a 57-year-old person are in the interval [3.575, 4.257] and the deterministic amount of premium is 3.896. Also, the net premiums for the average risk aversion mode (β =0.75) is 3.988. Also, these results were compared with the random method, which indicates the validity of the proposed fuzzy method.

Interest rates fluctuate over time due to changes in monetary, fiscal and foreign exchange policies, and this fluctuation can affect the determination of premiums, reserves and liabilities of insurance companies. This is especially important for life insurance products due to their long-term nature and the possibility of higher interest rate fluctuations during the policy period. Therefore, it is necessary to be considered the interest rate risk and uncertainty in life insurance products by the regulator and insurance companies. In this regard, using the fuzzy interest rate, the permitted range for the interest rate can be considered that insurance companies, taking into account their risk aversion, to determine the amount of premium in the desired period.JEL Classification: G22, C02, C63.